| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
[ destruct
- elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
+ elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
<(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
| elim (IHL12 … HLK1) -L1 /3 width=3/
]
-| #L1 #L2 #V1 #V2 #W1 #W2 #l #HV1 #HVW1 #HW12 #HW2 #HWV2 #_ #IHL12 #K1 #e #H
+| #L1 #L2 #W #V #W1 #V2 #l #HV #HW #HW1 #HV2 #_ #IHL12 #K1 #e #H
elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
[ destruct
- elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
+ elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
<(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
| elim (IHL12 … HLK1) -L1 /3 width=3/
]
]
-qed.
+qed-.
(* Note: the constant 0 cannot be generalized *)
lemma lsubsv_ldrop_O1_trans: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
[ destruct
- elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
+ elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
<(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
| elim (IHL12 … HLK2) -L2 /3 width=3/
]
-| #L1 #L2 #V1 #V2 #W1 #W2 #l #HV1 #HVW1 #HW12 #HW2 #HWV2 #_ #IHL12 #K2 #e #H
+| #L1 #L2 #W #V #W1 #V2 #l #HV #HW #HW1 #HV2 #_ #IHL12 #K2 #e #H
elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
[ destruct
- elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
+ elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
<(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
| elim (IHL12 … HLK2) -L2 /3 width=3/
]
]
-qed.
+qed-.